ECON 206 MACROECONOMIC ANALYSIS Roumen Vesselinov Class # 5

Transcription

1 ECON 206 MACROECONOMIC ANALYSIS Roumen Vesselinov Classs # 5

2 A Model of Production Chapter 4 (2 of 2)

3 Our object tives today Last time, part 1 of Chapter 4: Set up and solve a macroeconomic model Think about constant returns to scale and diminishing marginal productivity of factors like labor and capital This time, part II: Use our model to try and understand differences in GDP per person across countries (and fail miserably at first!) Gauge the importance of physical capital ( K ) versus total factor productivity ( A ) in explaining those differences in GDP per person, and talk about A

4 A recap of last class: Our model takes factors capital, K, and labor, L, as inputs and returns output, t Y The special functional form that describes output so well, the Cobb-Douglas production function, tells us that In words: output per pers on, y, equals a productivity constant, A, times capital per person, k, to the one-third y will be higher if A or k is higher But there are diminishing worker, k returns to scale in capital per

5 We now use this model to understand international differences in GDP per capita Let us imagine that y is GDP per capita rather than ice cream per capita; and k is capital per person, where capital includes all housing, factories, tools, etc. Then GDP per capita should be proportional p to k 1/3, What about productivity,? For now, let s assume that t, so that

6 To sum up: Our pro ocedure will be to... Measure y = output per person in each country, and also measure k = capital per person See what our model tells is, using this formula: us y ought to be, based on what k (Remember that we have assumed that.) Express everything in U.S. levels for easier comparison: Divide each country s k = K/L by the U.S. s k = K/L, so other countries results are X percent of U.S. level, where X can be less than 1.00, wh hich means lower than the U.S.

7 Country Capital per person, k USA Japan Brazil Predicted Actual GDP per GDP per person, y = k 1/3 person Given = 30% more k, Japan should have =10% more y than the U.S., butithas = 26% less! Brazil should have = 40% less y than the U.S., but it has = 78% less!

8 How can we see these patterns in a broad group of countries all at once? For each country, Let s graph its actual GDP per capita along the horizontal axis And graph the predicted GDP per capita from the model along the vertical axis

9 This 45 o line is how the data should appear if the model is accurate

10 What patterns are emerging? There are differences in capital per person, k, across countries, just as there are differences in GDP per capita, y But these differences in k do not explain the differences in y very well! For some rich countries with lots of capital per worker, like Japan, the model predicts very high GDP per person, higher than actually exists For many other countrie es with relatively little k, the model also predicts GDP per person than is higher than we actually observe

11 Why is the model fa ailing to fit the data? We do see big differences in capital per worker... But by design, these observed differences in physical capital across countries ca an only do so much because capital has diminishing marginal productivity Why? Think of extra mach hines sitting idly as ice cream workers are too busy with other machines Mathematically: In our model, y = k 1/3, so what do our growth rules say about gy and gk? gy = gk / 3 < gk. In words, output per person can t rise as fast as capital per person so differences we see in k translate into smaller differ rences in y, too small to fit reality, it seems

12 What can we do about this poor fit? Change the exponent on n y = k 1/3? Not a good idea Practically, choosing a larger power would only help us explain low y in developing countries, not low y in Japan or similar rich countries that have lots of k but also low y Also, we chose the power on k, 1/3, for a reason it fits the data. So we don t want to change it What about productivity,

13 For the model to fit, we must consider productivity differences We typically call Total Factor Productivity or TFP because it raises outpu for any combination of factors: TFP also raises GDP per capita for any level of capital per person: But what is? Is it a measurable input? We know it exists, but we can t really measure it, other than by backing it out of output and inputs

14 We proceed by defining TFP as the residual: what s left over We will assume that our model is correct, so TFP must account for unexplained differences in GDP per person Mathematically, we ll measure actual GDP per capita, then fit the model and define A as what s left after k 1/3 : So TFP is the measuree of our ignorance, and not really a real variable about which we have independent knowledge, such as capital or labor but it does measure how productiv vely economies use their factors

15 Examining total fa actor productivity (TFP) by country offers new insights Country Actual GDP per person USA Japan Brazil k 1/3 Implied TFP, A = y/k 1/ Our new interpretation is that TFP the efficiency with which countries combine capital and labor is lower in countries like Japan, and lower still in countries like Brazil

16 International differences in total factor productivity are large, and TFP clearly varies with income per capita

17 What does lower TFP mean for a country s production? We examine y versus k output per person given capital per person At some level of capital per person, The country with the higher h level l of productivity, A1 Will have higher h output t per person than the country with the lower level of A2 output per person, y y = A 1k 1/3 A1> A2 y = A2k 1/3 capital per person, k

18 What can we say about the relative importance of TFP? Differences in total factor productivity are responsible for rough hly two-thirds thi (67%) of differences in GDP per capita, y, across countries The remainder, one-third (33%), is associated with differences in capital per person, k That means producti vity matters a lot! How do we see this decomposition?

19 Write down GDP per capita for a rich country and a poor country Take the ratio of these equations 45 = 10 F d t fi d th t y is 10 ( ) = 2 x 4.5 f t f 45 diff i From data, we find that a factor-of-45 difference in 2/3 composed of a factor-of-of-10 difference in A and a factor-of-4.5 difference in k. And 10 is about twice of , soproductivity differences account for 2/3 of income differences

20 Next time: Since productivity ma atters so much, why are some countries more efficient than othe ers?